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frozen [14]
3 years ago
9

Solve the exponential equation by taking the logarithm on both sides. 5^(x+8)=7

Business
1 answer:
rodikova [14]3 years ago
7 0
<h2>Answer:</h2>

x = (log₅7) - 8

<h2>Explanation:</h2>

<em>Given;</em>

5^{x+8} = 7

<em>Take log of both sides;</em>

log₁₀(5^{x+8}) = log₁₀7               -------------(ii)

<em>From the laws of logarithm remember that;</em>

logₐ xⁿ = n logₐ x

<em>Equation (ii) can then be written as;</em>

(x + 8)log₁₀5 = log₁₀7

<em>Divide both sides by log₁₀5</em>

(x + 8) = \frac{log_{10}7}{log_{10}5}                -----------(iii)

<em>From the laws of logarithm, remember that;</em>

\frac{log_{a}x}{log_{a}y} = log_yx

<em>Equation (iii) can thus be written as;</em>

(x + 8) = log₅7

x + 8 = log₅7

<em>Make x subject of the formula;</em>

x = (log₅7) - 8

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