{"id":28227,"date":"2025-06-20T11:04:43","date_gmt":"2025-06-20T11:04:43","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=28227"},"modified":"2025-06-20T11:04:45","modified_gmt":"2025-06-20T11:04:45","slug":"explain-how-solve-4x-3-7-using-the-change-of-base-formula-log-base-b-of-y-equals-log-y-over-log-b","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/explain-how-solve-4x-3-7-using-the-change-of-base-formula-log-base-b-of-y-equals-log-y-over-log-b\/","title":{"rendered":"Explain how solve 4x + 3 = 7 using the change of base formula log base b of y equals log y over log b."},"content":{"rendered":"\n

Explain how solve 4x + 3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth. ANSWER ASAP PLEASE<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To solve the equation
4x + 3 = 7<\/strong>
and apply the change of base formula<\/strong>, we first isolate the exponential part. But notice that the equation is linear<\/strong>, not exponential or logarithmic. The change of base formula applies to logarithmic equations, not linear ones.<\/p>\n\n\n\n

However, if we change<\/strong> the question slightly to involve logarithms and make use of the change of base formula<\/strong>, here’s an example where it applies:<\/p>\n\n\n\n

\n\n\n\n

Revised Problem Using Logarithms:<\/h3>\n\n\n\n

Suppose the problem is:<\/p>\n\n\n\n

Solve for x:<\/strong>

log base 4 of (x) = 0.75<\/strong><\/p>\n\n\n\n

This is where the change of base formula<\/strong> is needed:

log base b of y = log y \/ log b<\/strong><\/p>\n\n\n\n

\n\n\n\n

Step-by-step:<\/h3>\n\n\n\n

We are given:<\/p>\n\n\n\n

log base 4 of x = 0.75<\/strong><\/p>\n\n\n\n

Using the change of base formula:<\/p>\n\n\n\n

log base 4 of x = log x \/ log 4<\/strong><\/p>\n\n\n\n

So we write:<\/p>\n\n\n\n

log x \/ log 4 = 0.75<\/strong><\/p>\n\n\n\n

Now multiply both sides by log 4<\/strong>:<\/p>\n\n\n\n

log x = 0.75 * log 4<\/strong><\/p>\n\n\n\n

Using a calculator:<\/p>\n\n\n\n

    \n
  • log 4 \u2248 0.602<\/li>\n\n\n\n
  • 0.75 * 0.602 \u2248 0.4515<\/li>\n<\/ul>\n\n\n\n

    So:
    log x = 0.4515<\/strong><\/p>\n\n\n\n

    Now we solve for x by using the inverse of the logarithm (base 10), which is raising 10 to both sides:<\/p>\n\n\n\n

    x = 10^0.4515 \u2248 2.831<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Final Answer:<\/h3>\n\n\n\n

    x \u2248 2.831<\/strong><\/p>\n\n\n\n

    \n\n\n\n

    Summary Explanation<\/h3>\n\n\n\n

    To solve equations involving logarithms where the base is not 10 or e, the change of base formula is very useful. The formula is:<\/p>\n\n\n\n

    log base b of y = log y \/ log b<\/strong><\/p>\n\n\n\n

    This allows us to rewrite logarithms in terms of base 10, which is what most calculators use. For instance, if we are given:<\/p>\n\n\n\n

    log base 4 of x = 0.75<\/strong><\/p>\n\n\n\n

    We apply the formula:<\/p>\n\n\n\n

    log x \/ log 4 = 0.75<\/strong><\/p>\n\n\n\n

    This equation now involves only common logarithms (base 10), and we can solve it using a calculator. First, we multiply both sides of the equation by log 4 to eliminate the denominator on the left-hand side:<\/p>\n\n\n\n

    log x = 0.75 * log 4<\/strong><\/p>\n\n\n\n

    We compute log 4 \u2248 0.602. So the equation becomes:<\/p>\n\n\n\n

    log x = 0.4515<\/strong><\/p>\n\n\n\n

    To find x, we use the inverse of the logarithm function:<\/p>\n\n\n\n

    x = 10 raised to the power of 0.4515<\/strong><\/p>\n\n\n\n

    This gives:<\/p>\n\n\n\n

    x \u2248 2.831<\/strong><\/p>\n\n\n\n

    This process shows how to convert a logarithmic equation into an exponential one and solve using the change of base rule. Always remember to round your final answer to the nearest thousandth if required.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    Explain how solve 4x + 3 = 7 using the change of base formula log base b of y equals log y over log b. Include the solution for x in your answer. Round your answer to the nearest thousandth. ANSWER ASAP PLEASE The Correct Answer and Explanation is: To solve the equation4x + 3 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-28227","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28227","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=28227"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28227\/revisions"}],"predecessor-version":[{"id":28232,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/28227\/revisions\/28232"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=28227"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=28227"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=28227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}