Question

lesson 7.2 - log vs exponent conversions
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7.2 hw - log vs exponent
score: 16.33/19 answered: 9/10
question 10
solve:
\\(\log_{4}(x) + 5 = 8\\)
\\(x =\\) input box calculator interface: basic, funcs, trig buttons, etc. enter a mathematical expression more..

Explanation:

Step1: Isolate the logarithmic term

Subtract 5 from both sides of the equation $\log_{4}(x) + 5 = 8$ to get $\log_{4}(x)=8 - 5$.
$\log_{4}(x)=3$

Step2: Convert logarithmic to exponential form

Recall the definition of a logarithm: if $\log_{b}(a)=c$, then $b^{c}=a$. Here, $b = 4$, $c = 3$, and $a=x$. So we convert $\log_{4}(x)=3$ to exponential form: $x = 4^{3}$.

Step3: Calculate the value of $4^{3}$

$4^{3}=4\times4\times4 = 64$.

Answer:

$x = 64$